Identifying polynomial variables

I hope someone can help. I'm trying to solve for the following problem:

So far I have identified the value for c, which is 1. And then I plugged in the points (3,12) in order to isolate a and b. As follows:

I'm struggling to solve for a and b. When I sub a into b, or visa versa, I don't get an actual number. Could someone please go through the steps on how to solve for these two variables? According to the textbook, the solution for a = -11/9 and b = 22/3.

Re: Identifying polynomial variables

Originally Posted by otownsend

So far I have identified the value for c, which is 1. And then I plugged in the points (3,12) in order to isolate a and b. As follows:
I'm struggling to solve for a and b. When I sub a into b, or visa versa, I don't get an actual number. Could someone please go through the steps on how to solve for these two variables? According to the textbook, the solution for a = -11/9 and b = 22/3.

You posted this as a calculus question.
So the derivative, $2ax+b=0)$ at $(3,12)$.